London has been battered by 50mph winds that have felled trees and caused travel chaos. Powerful gusts swept across the capital as the Met Office issued a yellow "be aware" weather alert for most of the country.

“I don’t think I’m lacking in pluck,” said Chloe Smith, after confirming she volunteered to take her clothes off for a life-drawing class.

But did she really go au naturel for the sake of art? She said “um” and er” for a full 10 seconds before pleading: “Can’t you just write, ‘She dissolves into a fit of giggles’?” Certainly not.

Rumours that the government minister responsible for public service reform and Whitehall efficiency has been part-timing as a nude model is something Evening Standard readers probably want to know more about.

“I offered to do it for a drawing circle but the truth is my services were not required because another model volunteered. After all the giggles and the salacious rumours that’s the truth.”

True or not, the point was made that the MP for Norwich North is not lacking in spirit, and is far removed from the cliché of the starchy, blue-rinse Tory lady. Ms Smith, 30, has become the poster girl of Conservative modernisers — a status that attracts envy and bitchiness from older rivals for scarce ministerial posts in the Coalition.

Her job is at the heart of Government, in the Cabinet Office, in a team tasked with identifying savings in other departments worth £8 billion by the end of this financial year.

“There’s an enormous job to do in reducing the Government’s wasteful spending,” said the former Deloitte management consultant. “It’s welcomed by taxpayers.”

With a Cabinet row raging between those who want to stave off cuts in their own back yards by slashing the welfare bill further, Ms Smith takes a hard line on ministers who are finding Whitehall belt-tightening tough going. “We are in incredibly tough economic times and it would be crass to say that it’s just government finding that hard — everybody is finding it hard,” she said.

“People are worried about the cost of living and the cost of plenty more. The least we can do is reduce the cost of government.”

Would she disagree with Defence Secretary Philip Hammond, who has claimed military spending cannot be cut any further? “I will leave that to a Cabinet discussion,” she replied.

She gave another flash of steel ruminating over the Eastleigh by-election defeat. It should not, she said, suggest abandoning the modernising appeal to new, younger Conservative supporters to appease a disillusioned core vote. “A party that aspires to serve the whole country has to do all of those things.”

Ms Smith was born during the Falklands War in 1982. Her earliest political memory is of John Major’s leadership battle. It was not until the Blair years that she became interested in politics, while trying as a teenager at a Norfolk comprehensive to set up a youth forum in the county.

“My parents are incredibly self-reliant and hard working,” she said. “My father was a furniture designer and cabinet maker who ran his own business, while my mother was a teacher.

“The things that make me a Conservative are a deep respect for the individual, but also for individuals taking responsibility.”

She became an MP in a 2009 by-election and a minister in 2011. She all but confirmed a Thick of It-style rumour that the Prime Minister wrongly believed she was a trained chartered accountant when he picked her for a job at the Treasury.

“People often make that mistake about people who have worked for the big firms,” she said, plainly not denying it. She left the Treasury weeks after a car-crash interview with Jeremy Paxman on Newsnight, when he mocked her for being unable to say when a sudden U-turn on fuel tax was decided. She shrugged off the experience as just a “bad day at the office”, adding: “I suspect I joined a club.”

At the Cabinet Office her role includes rushing through the legislation to end primogeniture in the royal succession — a reform made even more vital by the Duchess of Cambridge’s apparent hint that she and Prince William are expecting a daughter.

“Obviously there’s a lot of excitement and speculation, but regardless of whether it’s a boy or a girl, the great thing is that for first time, their baby will have an equal claim — if they have a girl, she will be our Queen.”

Despite the Lord Rennard furore, Ms Smith said she had never experienced sexism, let alone groping, at Westminster. And she appealed to women not to be put off a career in politics. “I’m passionate about the work I do,” she said. “I would not want other women to think they should not take a chance.”

This year she will marry ex-soldier Sandy McFadzean, 34, a financial consultant and triathlete. She proposed after a four-month romance. “We just knew we had each found the right person,” she said. Naturally, the wedding is being planned on a spreadsheet.

With all that going on, she still finds time to attend life-drawing classes occasionally. “You find a whole range of models of all shapes and sizes,” she grinned, without embarrassment. “Men and woman, old and young, in a variety of different poses. That’s the point really, to draw the human form in all its variety.

“I don’t imagine I can show you any of my sketches to prove the point, though, can I?”